Problem: Express this quotient in scientific notation: ${\frac{4.000\times 10^{4}} {8.0\times 10^{4}}}$
Solution: Start by collecting like terms together. $= {\frac{4.000} {8.0}} \times{\frac{10^{4}} {10^{4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.50 \times 10^{4\,-\,4}$ $= 0.50 \times 10^{0}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.50$ is the same as $5.00 \div 10$ , or $5.00 \times 10^{-1}$ $ = {5.00 \times 10^{-1}} \times 10^{0} $ $= 5.00\times 10^{-1}$